Russia warned on Wednesday that any attack on its citizens in Ukraine would be considered an attack on Russia itself, as the Ukrainian government said it had resumed its "antiterrorist" operation against pro-Russian militants in the eastern part of the country.

The escalating rhetoric comes amid growing signs that the agreement reached last week in Geneva between the U.S., European Union, Russia and Ukraine, laying out steps to reduce tension, was headed for failure. Its collapse would escalate a race between...